I also have to agree that horses are herd animals. My family kept a horse for a year alone and had goats for company. Even though the goats kept my horse some company, you could still tell she was just off. When we finally got our second horse, she went back to her old self and began acting like a horse again.
I would definitely consider getting either goats or another horse to keep the first one company. I don't have much experience with minis, but I do know it will not be happy in a backyard all by itself!
Also, horses tend to turn an area into a mud pit in a matter of days. What their hooves don't destroy, their mouths will. This is the number one reason we decided NOT to fence in our front yard as we did not want it turn into mud. However, by rotating pastures, you can prevent this.
If your entire yard is wet, then that may cause problems with the horse's hooves. However, if there are areas that stay dry such as the top of a hill, then the horse will be able to hang out in those areas during the wet season. For example, our pasture is on a hill. There is a flat part at the bottom of the hill which is always muddy and a flat part at the top. Our horses tend to hang out more at the top of the hill where it is dry. This situation works pretty well, especially in really wet weather.
I don't know if this makes sense. I was a little distracted while writing it! My best advice before purcahsing something like a horse is research, research, research! horses are a lot of fun, but small mistakes can potentially lead to huge problems! Chances are you will inevitably make some mistakes, but researching will help you avoid so many others!